Chain rule and side parameter
The essential ingredient of Jorgensen's work in  is a detailed analysis of how the pattern of isometric hemispheres bounding the Ford domain change as one varies the group. This idea can be found in his preceding work  on the infinite cyclic Kleinian groups. (See the work  due to Drumm and Poritz for its detailed exposition and generalization.) In this chapter we first describe the “chain rule for isometric circles” (Lemma 4.1.2), which affords a foundation on the analysis, and then we introduce the key notion of Jorgensen's side parameter (Definition 4.2.9) and prove various of its properties.
KeywordsTriangle Inequality Chain Rule Parallel Argument Elliptic Generator Parallel Translation
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